What Is a Conjecture in Mathematics? Definition, Example & Counterexample #3259414 (License: Personal Use)

This educational slide defines a conjecture as an informed hypothesis derived from observed data or examples, emphasizing that a single counterexample suffices to falsify it. It illustrates this using the common misconception that all prime numbers are odd, citing 1, 3, 5, 7, 11, and 13 as apparent support, then refuting it with the counterexample of 2-prime yet even. The visual design uses geometric background patterns to enhance readability and engagement for classroom or online learning contexts.

Used in mathematics education materials-such as PowerPoint lectures, Khan Academy-style videos, or curriculum-aligned web pages-to introduce logical reasoning and proof concepts. Matches user intent for students or educators seeking foundational understanding of conjectures and falsifiability.